We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our algorithm showing provable sample recovery in a linear model setting. The algorithmic insight obtained from our analysis extends to more general settings often considered in practice. Experimentally, we outperform previously proposed posterior sampling algorithms in a wide variety of problems including random inpainting, block inpainting, denoising, deblurring, destriping, and super-resolution.

翻译：我们提出了首个利用预训练潜扩散模型求解线性逆问题的框架。此前提出的算法（如DPS和DDRM）仅适用于像素空间扩散模型。我们从理论上分析了所提出的算法，证明了在线性模型设定下样本的可证明恢复性。由该分析获得的算法洞见可扩展至实践中常见的更一般化设定。在实验方面，我们在包括随机修补、块状修补、去噪、去模糊、去条纹以及超分辨率在内的广泛问题中，均超越了此前提出的后验采样算法性能。